After having this happen to me in TWO zones so far, and having heard of numerous others succumbing to the same bug, and getting NO help from Carbine's "support" after submitting a ticket TWICE on it, I thought I'd post a bit of a "public safety" message to those who are Settlers.
There is a bug with the Public Safety missions where if you take the "WANTED" missions and complete them BEFORE the Public Safety missions come up in your Datachron, you will NOT get credit for the Public Safety missions no matter how many times you kill the mob.
This is a very specific bug, and easily to duplicate. The best example is for Hagus the Collosus in Whitevale. There, the "WANTED" mission shows up on the bounty board at Thermock Hold, your first quest hub upon entering the zone. However, the Public Safety mission won't show up in your Datachron until you get to the Gas and Guzzle, which is further into the zone. Upon receiving the Public Safety mission in your Datachron it will point you BACK to Thermock Hold to take it from the bounty board so that you can complete it. Problem is, you more than likely already took it while in Thermock and finished it meaning you can no longer get the "WANTED" mission to satisfy the requirements for the Public Safety mission.
But it's not only that simple. If you take the "WANTED" mission but do not kill the mob BEFORE you get the mission in your Datachron, it will not complete then either.
The only way to avoid this bug is to take NO bounty board missions until you are assured you have a Public Safety mission for the corresponding mob on the bounty board first. Meaning, you check your Public Safety missions to see which mobs you are supposed to kill FIRST, THEN take the corresponding mission from the bounty board next.
Failing to do this can result in you not being able to complete a zone and ergo, not being able to claim the Settler completion rewards for the zone at all.
In my case, this happened to me for BOTH Celestion and Whitevale before I figured out precisely how the problem was occurring.
Additional note for the mods: This doesn't need to be moved and hidden under the rug like so many other bug reports. It needs to stay somewhere EVERYONE can see it so that the way to avoid experiencing this bug can be made clear. In theory, hiding this would cause more people to suffer the same bug, and submit MOIRE tickets to Carbine thereby increasing the workload.
On a final note, it'd be really swell if customer support would actually credit my Warrior on my account for killing Drugaur the Rotted in Grimhold and Hagus the Collosus in Whitevale since I can no longer claim the completion rewards for either zone.